Continuation of relative periodic orbits in a class of triatomic hamiltonian systems
Guillaume James, Pascal Noble, Yannick Sire (2009)
Annales de l'I.H.P. Analyse non linéaire
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Displaying similar documents to “Estimation of the amplitude of resonance in the general standard map.”
Continuation of relative periodic orbits in a class of triatomic hamiltonian systems
Localization of periodic orbits of autonomous systems based on high-order extremum conditions.
Starkov, Konstantin E. (2004)
Mathematical Problems in Engineering
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An extension of the Artin-Mazur theorem.
Kaloshin, Vadim Yu. (1999)
Annals of Mathematics. Second Series
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Seventy-five years of global analysis around the forced pendulum equation
Mawhin, Jean
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Existence of periodic solutions and homoclinic orbits for third-order nonlinear differential equations.
Motlagh, O. Rabiei, Afsharnezhad, Z. (2003)
International Journal of Mathematics and Mathematical Sciences
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Invariant tori for periodically perturbed oscillators.
Carmen Chicone (1997)
Publicacions Matemàtiques
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The response of an oscillator to a small amplitude periodic excitation is discussed. In particular, sufficient conditions are formulated for the perturbed oscillator to have an invariant torus in the phase cylinder. When such an invariant torus exists, some perturbed solutions are in the basin of attraction of this torus and are thus entrained to the dynamical behavior of the perturbed system on the torus. In particular, the perturbed solutions in the basin of attraction of the invariant...
Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity
Zhen Wang, Wei Sun, Zhouchao Wei, Shanwen Zhang (2017)
Kybernetika
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Periodic parametric perturbation control and dynamics at infinity for a 3D autonomous quadratic chaotic system are studied in this paper. Using the Melnikov's method, the existence of homoclinic orbits, oscillating periodic orbits and rotating periodic orbits are discussed after transferring the 3D autonomous chaotic system to a slowly varying oscillator. Moreover, the parameter bifurcation conditions of these orbits are obtained. In order to study the global structure, the dynamics...